A sequence an of integers consists of n elements. For a given number k find a non-empty subsequence ai, ai+1, ... ai+m of consecutive elements of the sequence an, such that the sum of its elements as close as possible to k.

Input

The first line contains two integers n and k (1 ≤ n ≤ 500000, -109 ≤ k ≤ 109) - number of elements in the sequence and the desired sum. The second line is followed by n integers ai (-109 ≤ ai ≤ 109) - the elements of the sequence.

Output

Print one number |k – l| (absolute difference of k – l), where l is the total sum on optimum segment of the sequence.